Download Math Apps 6.4 Guided Notes

Name: _____________________________
Math Apps 6.4 Guided Notes
Ratio, Proportion and Variation
Ratios
A ____________________ is a comparison of two quantities using division.
For two nonzero numbers, a and b, the ______________________ _ is written as a:b (read a to b) or
a
b
Example Problem
According to the Sporting Goods Manufacturers’ Association, 95.1 million Americans participate in
recreational swimming, 56.2 million Americans participate in recreational biking, 52.6 million Americans
participate in bowling, and 44.5 million Americans participate in freshwater fishing. Find each:
(a) The ratio of recreational swimmers to recreational bikers
(b) The ratio of people who fish to people who bowl
Proportions
A __________________________ is a statement of equality of two ratios.
For example, the ratio of 4:7 and 8:14 can be written as a proportion as shown.
4
8

7 14
Two ratios form a proportion if the cross products of their numerators and denominators are equal.
a c
 , if ad  bc.
b d
Example Problems
Decide if each proportion is true or false.
Solve the proportion for x.
Solve the proportion:
While on a spring break trip, a group of friends burns 12 gallons of gas in the first 228 miles, then stops
to refuel. If they have 380 miles yet to drive, and the SUV has a 21-gallon tank, can they make it without
refueling again?
As part of a research project, a biology class plans to estimate the number of fish living in a lake thought
to be polluted. They catch a sample of 35 fish, tag them, and release them back into the lake. A week
later, they catch 80 fish and find that 5 of them are tagged. About how many fish live in the lake?
Variation
A quantity y is said to _________________________ with x if there is some nonzero constant k so that
y = kx. The constant k is called the __________________________.
Two quantities are often related in such a way that if one goes up, the other does too, and if one goes
down, the other goes down as well. This would show direct variation.
Example Problem
Suppose you earn $95 per day. Write a variation equation that describes total pay in terms of days
worked, and use it to find your total pay if you work 6 days and if you work 15 days.
The weight of a certain type of cable varies directly with its length. If 20 feet of cable weighs 4 pounds,
find k and determine the weight of 75 feet of cable.
Variation CONT.
A quantity y is said to _________________________ with x if there is some nonzero constant k so that
y=
k
.
x
Example Problems
The time it takes to drive a certain distance varies inversely with the speed, and the constant of
proportionality is the distance. A family has a vacation cabin that is 378 miles from their residence.
Write a variation equation describing driving time in terms of speed. Then use it to find the time it takes
to drive that distance if they take the freeway and average 60 miles per hour, and if they take the scenic
route and average 35 miles per hour.
In construction, the strength of a support beam varies inversely with the cube of its length. If a 12-foot
beam can support 1,800 pounds, how many pounds can a 15-foot beam support?